Controllability

Summary

A control system is controllable if every state can be steered to every other state by a suitable choice of the control. It is the first question of control theory: before asking how to steer well, one asks whether steering is possible at all. For linear systems $x' = A x + B u$ it is decided by the Kalman rank condition, and for systems without drift by the Chow–Rashevskii theorem.